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Let $\mathcal{B}$ be the basis of $\mathbb{P}_{3}$ consisting of the Hermite polynomials in Exercise $21,$ and let $\mathbf{p}(t)=7-12 t-8 t^{2}+12 t^{3}$ . Find the coordinate vector of $\mathbf{p}$ relative to $\mathcal{B}$ .

$[\vec{P}]_{B}=\left[\begin{array}{c}{3} \\ {3} \\ {-2} \\ {3 / 2}\end{array}\right]$

Calculus 3

Chapter 4

Vector Spaces

Section 5

The Dimension of a Vector Space

Vectors

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Lectures

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In mathematics, a vector (…

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Let $\mathcal{B}$ be the b…

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Let $\mathbf{p}_{1}(t)=1+t…

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The set $\mathcal{B}=\left…

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In $\mathbb{P}_{2},$ find …

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Let $p_{1}(x)=1+x, p_{2}(x…

05:44

For Problems $15-18$, dete…

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Let $\mathcal{B}=\left\{\m…

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Find a polynomial $p_{3}$ …

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Determine $T(\mathbf{v})$ …

04:47

work. Given the faces, that is, um, one one minus t. And to minus 40 us t squared. Yeah. So we have these three a nominal size. Our faces. So we honored to Right down. He up t in terms off. Coordinated back. Factor off P lifted two spaces. First down, Petey is seven miners on a safety plus re t squared. Get less. Dean owed one as p one and one minus TSP too. And do you mind us? 40 plus t squared as p three. So in order to get three t squared, the only the only way to get people can t squared is too is by using the p three. So at least we have to times p three by three. That way we can get three t squared minus well, t, that's sick. Only in this way we can get pretty squared. Otherwise, we don't have t squared in p to m p one. So And you too. We need to combine Pete even p three to get connective and activate e. And we What we have for Peter is negative t and we've already had we Robert He already had a negative 12 so the only thing we need to do is two times you to buy electric port so that he so that this this, uh, this is equal to negative for last 40 or teeth. Okay. So that our, uh, Osama off three p three milers, four p two will be well, give us negative 80. So, in terms off and then ask in terms off a constant term, we have one. But previous previous stabs our already give us, uh, to because six minus four would be too s o. The only thing we need to add is fight so that to minus to plus five will be seven, which is here. So our final answer will be first three p three minus 42 plus p one. Well, five, if you want. All right, So this is our by no answer.

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